# Interesting bouyancy theoretical question

1. Feb 2, 2010

### amnestic

Hello, I have a question

Lets say you have a container of water that weighs 10 pounds including the water/container material

and u have a 5 pound object that can float quite easily in that water

and u attach a piece of string to that object to the bottom of the container of water to the halfway point so that the object is suspended in the water at the midway point

Now if you were to put this contraption on a scale, will it weigh 15 pounds plus the weight of the string

or will it be between 10 to 15 pounds due to the bouyancy force upwards on the object

ENGAGE!

2. Feb 2, 2010

### Staff: Mentor

It would weigh 15 pounds plus the weight of the string. The bouyancy force is not acting on the scale.

Let's say that the string has negligible mass and displaces a negligible volume water, the float weighs 5 pounds and a volume equal to 6 pounds of water, the water weighs 9 pounds, and the container weighs 1 pound.

A free body diagram of the float shows that the tension in the string (1 lb down) is equal to the force of the water on the float (6 lb up) minus the weight of the float (5 lb down). A free body diagram of the water shows that the force of the container on the water (15 lb up) is equal to the weight of the water (9 lb down) plus the force of the float on the water (6 lb down). A free body diagram of the container shows that the force of the scale on the container (15 lb up) is equal to the force of the water on the container (15 lb down) plus the weight of the container (1 lb down) minus the tension in the string (1 lb up). A free body diagram of the scale shows that the force of the container on the scale is 15 lb up.

Last edited: Feb 3, 2010